Question

Let A= {1, 2, {3, 4,}, 5}. Which of the following statements are incorrect and why? 

(i) {3, 4}⊂ A 

(ii) {3, 4}}∈ A

(iii) {{3, 4}}⊂ A 

(iv) 1∈ A 

(v) 1⊂ A 

(vi) {1, 2, 5} ⊂ A 

(vii) {1, 2, 5} ∈ A 

 (viii) {1, 2, 3} ⊂ A 

(ix) Φ ∈ A 

(x) Φ ⊂ A 

(xi) {Φ} ⊂ A 

Answer 1

A = {1, 2, {3, 4}, 5} 

(i) The statement {3, 4} ⊂ A is incorrect because 3 ∈ {3, 4}; however, 3∉A. 

(ii) The statement {3, 4} ∈A is correct because {3, 4} is an element of A. 

(iii) The statement {{3, 4}} ⊂ A is correct because {3, 4} ∈ {{3, 4}} and {3, 4} ∈ A. 

(iv) The statement 1∈A is correct because 1 is an element of A. 

(v) The statement 1⊂ A is incorrect because an element of a set can never be a subset of itself. 

(vi) The statement {1, 2, 5} ⊂ A is correct because each element of {1, 2, 5} is also an element of A. 

(vii)The statement {1, 2, 5} ∈ A is incorrect because {1, 2, 5} is not an element of A. 

(viii) The statement {1, 2, 3} ⊂ A is incorrect because 3 ∈ {1, 2, 3}; however, 3 ∉ A. 

(ix) The statement Φ ∈ A is incorrect because Φ is not an element of A. 

(x) The statement Φ ⊂ A is correct because Φ is a subset of every set. 

(xi) The statement {Φ} ⊂ A is incorrect because Φ∈ {Φ}; however, Φ ∈ A.